Alexander groups of long virtual knots

被引：7

作者：

Silver, DS ^{[1
]}

Williams, SG ^{[1
]}

机构：

[1] Univ S Alabama, Dept Math & Stat, Mobile, AL 36688 USA

来源：

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS | 2006年 / 15卷 / 01期

基金：

美国国家科学基金会;

关键词：

virtual knot; Alexander group;

D O I：

10.1142/S021821650600435X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Alexander group systems for virtual long knots are defined and used to show that any virtual knot is the closure of infinitely many long virtual knots. Manturov's result that there exists a pair of long virtual knots that do not commute is reproved.

引用

页码：43 / 52

页数：10

共 50 条

[41] Graphing, homotopy groups of spheres, and spaces of long links and knots
Koytcheff, Robin
FORUM OF MATHEMATICS SIGMA, 2025, 13
[42] Nontrivial Alexander polynomials of knots and links
Friedl, Stefan
Vidussi, Stefano
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2007, 39 : 614 - 622
[43] On Milnor moves and Alexander polynomials of knots
Ishikawa, T
Kobayashi, K
Shibuya, T
OSAKA JOURNAL OF MATHEMATICS, 2003, 40 (04) : 845 - 855
[44] Braid presentation of virtual knots and welded knots
Kamada, Sechi
OSAKA JOURNAL OF MATHEMATICS, 2007, 44 (02) : 441 - 458
[45] Reduction of knots in thickened surfaces and virtual knots
F. G. Korablev
S. V. Matveev
Doklady Mathematics, 2011, 83 : 262 - 264
[46] Reduction of knots in thickened surfaces and virtual knots
Korablev, F. G.
Matveev, S. V.
DOKLADY MATHEMATICS, 2011, 83 (02) : 262 - 264
[47] Biquandles for virtual knots
Hrencecin, David
Kauffman, Louis H.
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2007, 16 (10) : 1361 - 1382
[48] VIRTUAL CROSSING NUMBERS FOR VIRTUAL KNOTS
Manturov, Vassily Olegovich
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2012, 21 (13)
[49] Virtual knots and links
Kauffman L.H.
Manturov V.O.
Proceedings of the Steklov Institute of Mathematics, 2006, 252 (1) : 104 - 121
[50] TWIST LATTICES AND THE JONES-KAUFFMAN POLYNOMIAL FOR LONG VIRTUAL KNOTS
Chrisman, Micah W.
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2010, 19 (05) : 655 - 675

← 1 2 3 4 5 →